Federico Poloni

Algorithms for Quadratic Matrix and Vector Equations

• Broschiertes Buch

Produktbeschreibung

This book is devoted to studying algorithms for the solution of a class of quadratic matrix and vector equations. These equations appear, in different forms, in several practical applications, especially in applied probability and control theory. The equations are first presented using a novel unifying approach; then, specific numerical methods are presented for the cases most relevant for applications, and new algorithms and theoretical results developed by the author are presented. The book focuses on "matrix multiplication-rich" iterations such as cyclic reduction and the structured doubling algorithm (SDA) and contains a variety of new research results which, as of today, are only available in articles or preprints.

Produktdetails

• Publications of the Scuola Normale Superiore 16
• Verlag: Edizioni Della Normale / Scuola Normale Superiore / Springer, Berlin
• Artikelnr. des Verlages: 80073053, 978-88-7642-383-3
• Seitenzahl: 250
• Erscheinungstermin: 11. November 2011
• Englisch
• Abmessung: 243mm x 154mm x 19mm
• Gewicht: 446g
• ISBN-13: 9788876423833
• ISBN-10: 8876423834
• Artikelnr.: 33574193

Inhaltsangabe

Linear algebra preliminaries.- Quadratic vector equations.- A Perron vector iteration for QVEs.- Unilateral quadratic matrix equations.- Nonsymmetric algebraic Riccati equations.- Transforming NAREs into UQMEs.- Storage optimal algorithms for Cauchy-like matrices.- Newton method for rank-structured algebraic Riccati equations.- Lur'e equations.- Generalized SDA.- An effective matrix geometric mean.- Constructing other matrix geometric means.

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Linear algebra preliminaries.– Quadratic vector equations.– A Perron vector iteration for QVEs.– Unilateral quadratic matrix equations.– Nonsymmetric algebraic Riccati equations.– Transforming NAREs into UQMEs.– Storage optimal algorithms for Cauchy-like matrices.– Newton method for rank-structured algebraic Riccati equations.– Lur'e equations.– Generalized SDA.– An effective matrix geometric mean.– Constructing other matrix geometric means.